Nuclear Physics - Nuclear instability and Radius Flashcards
Where on N/Z graph are alpha, beta plus and beta minus emitters found
Alpha - near the top of the line of stability
Beta minus - to the left of the line of stability
Beta plus - to the right of line of stability
When is a nucleus unstable
If it has too many:
Protons
Neutrons
Nucleons
Energy
N/Z graphs and stability for light isotopes with Z<20
Nuclei tend to be stable
Follow straight line N=Z
What must happen for heavy isotopes with Z>20 to be stable
The neutron-proton ratio increases
Stable nuclei must have more neutrons than protons
What happens in the nucleus at a short range of 1-3fm
Nucleons are bound by the strong nuclear force
What happens below 1fm
The strong nuclear force is repulsive in order to prevent the nucleus from collapsing
What happens at longer ranges in the nucleus
The electromagnetic force acts between protons and so more protons cause more instability
Why must more neutrons be added when more protons are added to the nucleus
To add distance between protons to reduce the electrostatic repulsion. The extra neutrons also increase the amount of binding force which helps to bind the nucleons together
where does electron capture occur on an N/Z graph
To the right of the stability line as the isotopes are proton rich
Which decay occurs when there are too many neutrons and what happens
Beta minus occurs
Neutron number decreases by 1
Proton number increases by 1
Equation for beta minus
neutron → proton + beta minus particle (electron) + antinuetrino
Which decay occurs when there are too many protons
Beta plus or electron capture occurs
Nucleon number stays constant
Neutron number increases by 1
Proton number decreases by 1
What happens in beta plus decay
A proton changes into a neutron and a beta plus particle (positron) and a neutrino are released
What happens in electron capture
An orbiting electron is taken in by the nucleus and combined with a proton. This forms a neutron and a neutrino
Which decay occurs when there are too many nucleons and what happens
Alpha emission occurs
Nucleon number decreases by 4
Both proton and neutron number decrease by 2
Which decay occurs when there is too much energy and what happens
Gamma emission occurs
This is usually after a different decay as the nucleus becomes too excited and has excess energy
How can you calculate and find out which decay occurs
Calculate the neutron:nucleon ratio or the neutron:proton ratio.
The more neutron rich nucleus with higher ratio undergoes beta minus etc….
What happens when a daughter nucleus is in an excited state
Emits remaining energy in the form of a gamma photon.
The nucleus quickly moves to its ground state either directly or via one or more lower energy excited states
What is the application of nuclear excited states
use of technetium-99m as a γ source in medical diagnosis.
What does the m in technetium-99m stand for
metastable - which means the nucleus exists in a particularly stable excited state
Which two ways can nuclear radius be measured
Rutherford scattering - closest approach method
Electron scattering
Describe the closest approach method
The alpha particle is fired at a thin sheet of gold foil with an initial KE.
The Rutherford scattering indicates there must be an electrostatic repulsion between alpha p and gold nucleus
At the point of closest approach, r, the repulsive force reduces the speed of alpha particles to 0 momentarily.
So initial KE of alpha particles is transferred to electric potential energy.
Equation for electric potential energy
EPE = charge1 x charge2 / 4pi x e0 x radius of closest approach
What does using KE = EPE to find nuclear radii assume
Assuming the alpha particle is fired at high energy
What does the closest approach method give
An estimate of the upper limit of the radius of the nucleus
Advantages of the closest approach method
Alpha scattering gives good estimate of upper limit for nuclear radius
Simple maths
Alpha particles are scattered only by protons and not all the nucleons in the nucleus
Disadvantages of the closest approach method
Does not give accurate value for radius as it is always an overestimate
Alpha particles contain hadrons which are affected by strong nuclear force
Gold nucleus will recoil as alpha particle approaches
Alpha particles have finite size whereas electrons can be treated as a point mass
Foil must be very thin to prevent multiple scattering
Alpha particles assumed to have same initial KE
What is the wave-like property of electrons
The ability to diffract
de Broglie wavelength of an electron =
Planck’s constant / mass of an electron x speed of electron
What does the equation for the de Broglie wavelength of an electron show
As the speed of the electron increases, the smaller the wavelength becomes
Describe what happens when a beam of electrons is directed at a thin target
Each electron will diffract around a nucleus.
A diffraction pattern is formed consisting of a central bright spot with dimmer concentric circles around it.
How can we find the size of the nucleus using the electron diffraction pattern
Plot a graph of intensity against diffraction angle.
Use the angle of first minimum intensity to determine size of nucleus
What are the advantages of electron scattering
More accurate than closest approach method
Gives direct measurement of the radius of a nucleus
Electrons are leptons so are not affected by strong nuclear force
Disadvantages of electron scattering
Electrons must be accelerated to very high speeds to maximise resolution as significant diffraction occurs when wavelength is similar size to nucleus.
Electrons can be scattered by both protons and neutrons and excessive scattering can make first minimum difficult to determine
actual radius of gold nucleus
6.6fm
Equation to find nuclear radius from electron scattering
sin theta = 1.22 x ( de Broglie wavelength / 2 x radius )
how to find nuclear radius from closest approach method
KE = EPE
rearrange to find r
remember the mass = 4u = 4 x mass of a proton
How does a graph of nuclear radius against nucleon number look
Graph starts with steep gradient at origin
Gradient decreases gradually to almost horizontal
What does the graph of nuclear radius against nucleon number show
As more nucleons added, nucleus gets bigger
Number of nucleons is not proportional to its size
What does the radius of nuclei depend on
The nucleon number because a more nucleons added, more space is occupied by nucleus so has a larger radius
Equation showing the relationship between radius and nucleon number
Nuclear radius = R0 x nucleon number ^ 1/3
Show that the density of a nucleus is constant and independent of the radius
V = 4/3 x pi x r^3
R = R0 x A^1/3
V = 4/3 x pi x R0^3 x A
density = m/v
m= = Au
density = Au / (4/3 x pi x R0^3 x A) = 3u / 4 x pi x R0^3
mass number A cancels out and remaining quantities are all constant
What does the nuclear density being significantly larger than atomic density suggest
Majority of atoms mass is in the nucleus
Nucleus is very small compared to the atom
Atoms must be mostly empty space
